This study examined a random stratified sample (n = 62) of teachers' work across eight institutions on three tasks that utilized dynamic statistical software. We considered how teachers may utilize and develop their statistical knowledge and technological statistical knowledge when investigating a statistical task. We examined how teachers…

This study is an exploration of teachers' engagement with concepts embedded in the normal distribution. The participants were a group of 290 in-service teachers enrolled in a teacher development program. The research instrument was an assessment task that can be described as an "unknown percentage" problem, which required the…

Information on the HIV/AIDS epidemic in Southern Africa is often interpreted through a veil of secrecy and shame and, I argue, with flawed understanding of basic statistics. This research determined the levels of statistical literacy evident in 316 future Mathematical Literacy teachers' explanations of the median in the context of HIV/AIDS…

Data distributions can be represented using different external representations, such as histograms and boxplots. Although the role of external representations has been extensively studied in mathematics, this is less the case in statistics. This study helps to fill this gap by systematically varying the representation that accompanies a task…

This paper identifies key concepts and issues associated with the reasoning of informal statistical inference. I focus on key ideas of inference that I think all students should learn, including at secondary level as well as tertiary. I argue that a fundamental component of inference is to go beyond the data at hand, and I propose that statistical…

In this reflective paper, we explore students' local and global thinking about informal statistical inference through our observations of 10- to 11-year-olds, challenged to infer the unknown configuration of a virtual die, but able to use the die to generate as much data as they felt necessary. We report how they tended to focus on local changes…

This paper is a personal exploration of where the ideas of "distribution" that we are trying to develop in students come from and are leading to, how they fit together, and where they are important and why. We need to have such considerations in the back of our minds when designing learning experiences. The notion of "distribution" as a lens…

Drawing conclusions from the comparison of datasets using informal statistical inference is a challenging task since the nature and type of reasoning expected is not fully understood. In this paper a secondary teacher's reasoning from the comparison of box plot distributions during the teaching of a Year 11 (15-year-old) class is analyzed. From…

Recent research into students' reasoning about variation refers specifically to notions of distribution that emerge. This paper reports on research where written responses, from tertiary introductory statistics students, were coded according to the level of consideration of variation. A hierarchy of reasoning about distribution is proposed, based…

Our primary goal is to design a micro world which aspires to research thinking-in-change about distribution. Our premise, in line with a constructivist approach and our prior research, is that thinking about distribution must develop from causal meanings already established. This study reports on a design research study of how students appear to…

This exploratory study, a one group pretest-posttest design, investigated the development of elementary preservice teachers' understandings of distribution as expressed in the measures and representations used to compare data distributions. During a semester-long mathematics methods course, participants worked in small groups on two statistical…

Variability stands in the heart of statistics theory and practice. Concepts and judgments involved in comparing groups have been found to be a productive vehicle for motivating learners to reason statistically and are critical for building the intuitive foundation for inferential reasoning. The focus in this paper is on the emergence of beginners'…

This paper examines ways in which coherent reasoning about key concepts such as variability, sampling, data, and distribution can be developed as part of statistics education. Instructional activities that could support such reasoning were developed through design research conducted with students in grades 7 and 8. Results are reported from a…